math help

What is 5/100 + 6/9?

What is 5/100 + 6/9?

Let's add

5
100
 +
6
9

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 5 by 9, and get 45, then we multiply 100 by 9 and get 900.

5/100 times 9

Do the same for the second term. We multiply 6 by 100, and get 600, then multiply 100 by 9 and get 900.

6/9 times 100

So now our fractions look like this:

45
900
 +
600
900

Step 2

Since our denominators match, we can add the numerators.

45 + 600 = 645

So the answer is:

645
900

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Nope! So now we try the next greatest prime number, 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

645
900
 ÷ 3 =
215
300

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 5...

Are both the numerator and the denominator evenly divisible by 5? Yes! So we reduce it:

215
300
 ÷ 5 =
43
60

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

Nope! So now we try the next greatest prime number, 47...

No good. 47 is larger than 43. So we're done reducing.

There you have it! Here's the final answer to 5/100 + 6/9

5
100
 +
6
9
 =
43
60
© 2014 Randy Tayler

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